AT_fps_24_k 順列

You are given an integer $ N $ . Consider permutations $ p = (p_1, p_2, \dots, p_N) $ of $ (1, 2, \dots, N) $ . Count how many such permutations satisfy the following condition, and output the result modulo $ 998244353 $ . - For every integer $ i $ such that $ 1 \leq i \leq N-1 $ , it must hold that $ \max(p_1, p_2, \dots, p_i) \neq i $ .

The input is given from standard input in the following format: > $ N $

Print the answer.

### Sample Explanation 1 The following $ 3 $ permutations $ p $ satisfy the condition: - $ (2,3,1) $ - $ (3,1,2) $ - $ (3,2,1) $ ### Constraints - $ 1 \leq N \leq 2.5 \times 10^5 $ - $ N $ is an integer